One way (of many) to solve this, is to calculate two values - $yesterday_start and $yesterday_end, and then check if the time stamp of the line in the log file lies between these two values. DateTime might prove useful. But beware of edge cases such as those days that switch from or to DST and other tricky business like that.

Another way could be to take $yesterday the way you do it now, and strip off the time information so that you only hold the date information. That's probably the easiest, because except for the way you obtaini $yesterday your code can run unaltered. But again, be careful that you don't run into problems on days that DST ends.

And finally, these days the three-arguments open (which you already use) with lexical filehandles is recommended. See perldoc open.

Ada Lovelace for the palindrome
Albert Einstein for having smelly feet
Alfred Nobel for his contribution to battlefield science
Burkhard Heim for providing the missing link between science and mysticism
Claude Shannnon for riding a unicycle at night at MIT
Donald Knuth for being such a great organist
Edward Teller for being the template for Dr. Strangelove
Edwin Hubble for pretending to be a pipe-smoking English gentleman
Erwin Schrödinger for cruelty to cats
Hedy Lamarr for weaponizing pianos
Hugh Everett for immortality, especially for cats
Isaac Newton for his occult studies
Kikunae Ikeda for discovering the secrets of soy sauce
Larry Wall for his website
Louis Camille Maillard for discovering why steaks taste good
Marie Curie for the shiny stuff
Nikola Tesla for the cool cars
Paul Dirac for speaking one word per hour when socializing
Richard Feynman for his bongo skills
Robert Oppenheimer for his in-depth knowledge of the Bhagavad Gita
Rusi P Taleyarkhan for Cold Fusion
Sigmund Freud for his Ménage ā trois
Theodor W Adorno for his contribution to the reception of jazz
Wilhelm Röntgen for the foundations of body scanners
Yulii Borisovich Khariton for the Tsar Bomba
Other (please explain why)